PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (200)
Orphanage
Unclass'd
Unproven (490)
Corrections (6)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: High Entry average rating: Medium
bounded (Definition)

Given a metric space $ (X, d)$, a subset $ A\subseteq X$ is said to be bounded if there is some positive real number $ M$ such that $ d(x, y)\leq M$ whenever $ x, y \in A$.

A function $ f : X \rightarrow Y$ from a set $ X$ to a metric space $ Y$ is said to be bounded if its range is bounded in $ Y$.



"bounded" is owned by PrimeFan. [ full author list (3) | owner history (2) ]
(view preamble)

View style:

See Also: totally bounded, alternate statement of Bolzano-Weierstrass theorem
Log in to rate this entry.
(view current ratings)

Cross-references: range, function, real number, positive, subset, metric space
There are 32 references to this entry.

This is version 8 of bounded, born on 2002-01-01, modified 2008-06-18.
Object id is 1167, canonical name is Bounded.
Accessed 5983 times total.

Classification:
AMS MSC: 54E35 (General topology :: Spaces with richer structures :: Metric spaces, metrizability)
Pending Errata and Addenda
None.
[ View all 2 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)